Related papers: Wavy spirals and their fractal connection with chi…
Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and…
In this article, we investigate the wave equation in spiral geometry and study the modes of vibrations of a one-dimensional (1-D) string in spiral shape. Here we show that the problem of wave propagation along a spiral can be reduced to…
It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation…
We present a particular class of solutions in Cartesian, cylindrical and spherical coordinates of the non-dispersive travelling wave variety that propagate an envelope of varying vorticity some of which include topological waves with…
We present a quantum theory for one-dimensional spin-1/2 multiferroics, where the vector spin chirality couples with the electric polarization. Based on exact diagonalization and bosonization, it is shown that quantum fluctuations…
In this paper we develop a theory for oscillatory integrals with complex phases. When $f:{\mathbb C}^n \to {\mathbb C}$, we evaluate this phase function on the basic character ${\rm e}(z) := e^{2\pi i x} e^{2\pi i y}$ of ${\mathbb C} \simeq…
Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be…
Pattern formation in ultra-cold quantum systems has recently received a great deal of attention.In this work, we investigate a two-dimensional model system accounting for the dynamics of trapped ions. We find a novel spiral wave which is…
Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have…
In this paper, we present numerical and experimental evidence of directional wave behavior, i.e. beaming and diffraction, along high-order rotational symmetries of quasicrystalline elastic metamaterial plates. These structures are obtained…
We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convection in a Rayleigh-B\'{e}nard system rotating uniformly about a vertical axis.…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
This paper investigates fractal dimension of linear combination of fractal continuous functions with the same or different fractal dimensions. It has been proved that: (1) $BV_{I}$ all fractal continuous functions with bounded variation is…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure…
Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the…
Droplet deformations caused by substrate vibrations are ubiquitous in nature and highly relevant for applications such as microreactors and single-cell sorting. The vibrations can induce droplet oscillations, a fundamental process that…
Stable periodic orbits in spiral galactic models that form families of precessing ellipses can create spiral density waves similar to those that are observed in real grand-design galaxies. We study the range in parameter space for which the…
Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems we present an approach that aims at characterizing quantitatively spiral-like elements in complex stripe-like patterns. The…
We study the spatial and temporal behavior of fluid in fully three-dimensional, general relativistic, magnetohydrodynamical simulations of both tilted and untilted black hole accretion flows. We uncover characteristically greater…